Analytical Investigation of Laminar Dusty Fluid Flow and Thermal Non-Equilibrium Heat Transfer in an Asymmetric Corrugated Channel with Heat Source

Abstract

This study presents an analytical investigation of the steady, two-dimensional laminar flow of an incompressible, viscous, dusty fluid contained within an asymmetric corrugated channel under thermal non-equilibrium conditions with internal heat generation. A stationary flat right wall and a stationary left wall with a sinusoidal corrugation define the channel geometry. The carrier fluid is embedded with a uniform distribution of rigid, small, spherical dust particles in the multi-phase system. A state of thermal non-equilibrium is explicitly considered to account for independent temperature variations between the phases. The governing nonlinear equations are non-dimensionalized and solved analytically using a regular perturbation technique for small wall corrugation amplitudes. The effects of the Reynolds number, Grashof number, Prandtl number and heat source parameter on the velocity and temperature distributions are investigated. The corresponding skin friction coefficients and local Nusselt numbers at both channel boundaries are also evaluated. The nonlinear influence and interaction of the governing parameters are further examined using Response Surface Methodology (RSM).